Question: Solve for $x$ and $y$ using substitution. ${-6x+6y = 6}$ ${y = 6x-9}$
Solution: Since $y$ has already been solved for, substitute $6x-9$ for $y$ in the first equation. ${-6x + 6}{(6x-9)}{= 6}$ Simplify and solve for $x$ $-6x+36x - 54 = 6$ $30x-54 = 6$ $30x-54{+54} = 6{+54}$ $30x = 60$ $\dfrac{30x}{{30}} = \dfrac{60}{{30}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {y = 6x-9}\thinspace$ to find $y$ ${y = 6}{(2)}{ - 9}$ $y = 12 - 9$ $y = 3$ You can also plug ${x = 2}$ into $\thinspace {-6x+6y = 6}\thinspace$ and get the same answer for $y$ : ${-6}{(2)}{ + 6y = 6}$ ${y = 3}$